On a stronger form of hereditary compactness in product spaces

1998/10/30 by Julian Dontchev, Dontchev, Julian, Maximilian Ganster +1
Mathematics · #54A05 #54B10 #54D30 #54G99 #FOS: Mathematics #General Topology (math.GN) #math.GN #msc:54A05 #msc:54B10 #msc:54D30 #msc:54G99

paper · pdf · doi:10.48550/arxiv.math/9810174

9 pages

arxiv created 1998/10/30 · arxiv updated 2009/11/30

Abstract

The aim of this paper is to continue the study of sg-compact spaces. The class of sg-compact spaces is a proper subclass of the class of hereditarily compact spaces. In our paper we shall consider sg-compactness in product spaces. Our main result says that if a product space is sg-compact, then either all factor spaces are finite, or exactly one factor space is infinite and sg-compact and the remaining ones are finite and locally indiscrete.

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